Unstable mixed convection in a heated horizontal porous channel

This paper presents a linear stability analysis of horizontal throughflow in a saturated porous channel bounded by parallel impermeable walls with heating provided from below and an insulated top. The linear stability analysis is carried out for general oblique rolls, leading to an eigenvalue problem for determining critical values for the Darcy-Rayleigh number as a function of the Péclet number, the wavenumber and the angular frequency. This problem is then solved using the Generalized Integral Transform Technique, such that the differential eigenproblem formulation analytically transformed into a matrix eigenvalue problem, which is then solved by traditional numerical algorithms. The results show that for longitudinal rolls, the only value of the angular frequency that leads to an unstable flow is zero, and that non-vanishing frequency values are obtained for oblique rolls. In addition critical values of the Darcy-Rayleigh number that lead to unstable solutions for different Péclet numbers, for different inclination angles are presented.